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Simplifying w2 + 6w + -131 = 0 Reorder the terms: -131 + 6w + w2 = 0 Solving -131 + 6w + w2 = 0 Solving for variable 'w'. Begin completing the square. Move the constant term to the right: Add '131' to each side of the equation. -131 + 6w + 131 + w2 = 0 + 131 Reorder the terms: -131 + 131 + 6w + w2 = 0 + 131 Combine like terms: -131 + 131 = 0 0 + 6w + w2 = 0 + 131 6w + w2 = 0 + 131 Combine like terms: 0 + 131 = 131 6w + w2 = 131 The w term is 6w. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6w + 9 + w2 = 131 + 9 Reorder the terms: 9 + 6w + w2 = 131 + 9 Combine like terms: 131 + 9 = 140 9 + 6w + w2 = 140 Factor a perfect square on the left side: (w + 3)(w + 3) = 140 Calculate the square root of the right side: 11.832159566 Break this problem into two subproblems by setting (w + 3) equal to 11.832159566 and -11.832159566.Subproblem 1
w + 3 = 11.832159566 Simplifying w + 3 = 11.832159566 Reorder the terms: 3 + w = 11.832159566 Solving 3 + w = 11.832159566 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + w = 11.832159566 + -3 Combine like terms: 3 + -3 = 0 0 + w = 11.832159566 + -3 w = 11.832159566 + -3 Combine like terms: 11.832159566 + -3 = 8.832159566 w = 8.832159566 Simplifying w = 8.832159566Subproblem 2
w + 3 = -11.832159566 Simplifying w + 3 = -11.832159566 Reorder the terms: 3 + w = -11.832159566 Solving 3 + w = -11.832159566 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + w = -11.832159566 + -3 Combine like terms: 3 + -3 = 0 0 + w = -11.832159566 + -3 w = -11.832159566 + -3 Combine like terms: -11.832159566 + -3 = -14.832159566 w = -14.832159566 Simplifying w = -14.832159566Solution
The solution to the problem is based on the solutions from the subproblems. w = {8.832159566, -14.832159566}
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